Union Square (and nearby)
Pros: Very central to pretty much everything you'll want to see, nice hotels, get more for your money hotel wise than Fisherman's Wharf.
Cons: Extremely busy area, quite a few beggars.
Hotels in the area that are budget friendly:
The Chancellor - this is really one of the best as far as your budget friendly options go. It is an older historic hotel with a great location.
The Powell - Steps from the Powell Street BART station and right next to the cable car turn around. You may want to specify you would like a room facing away from Powell Street or the cable cars may keep you up late and wake you very early. Very basic property. Location is the best thing is has going for it.
Hotel Adagio - Hipster scene, good restaurant, good location.
Westin St. Francis - If anyone is fimiliar with the Fatty Arbuckle scandal, this is the hotel! You can even stay in the notorious suite if you have the funds. That said, to those on a budget, you can often get this property on priceline for a very reasonable rate and you can't be the location.
If you have more to spend consider the following:
Campton Place - Luxury boutique hotel right on Union Square. Lovely on site restaurant.The
Four Seasons - The name pretty much tells you what the hotel is all about.
The Intercontiental - Just opened in 2008 and supposed to be extremely nice. Within walking distance of Union Square.
The St. Regis - Within walking distance but not technically Union Square. Great luxury hotel with spa to match.Don't hesitate to ask for info if you have a specific hotel in mind. It is impossible to list them all here!